Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 27, 2018; final manuscript received September 12, 2018; published online November 1, 2018. Assoc. Editor: Noel Brunetiere.

The ultrasonic technique is very effective in measuring lubricant film thickness in a noninvasive manner. To estimate the film thickness with reflection signals, two main ultrasonic models are often applied in cases of different film thicknesses; they are the spring model for thin films and the resonant model for thick films. However, when measuring oil film thicknesses distributed in a wide range, there is an inherent blind zone between these two models. This problem is especially prominent in online monitoring because the abrupt variation of film thickness is highly correlated with the occurrence of abnormal conditions. To address this issue, we further proposed a method using the phase spectrum of reflection coefficient which can cover a wide range of film thicknesses. The slight variation of reflection signal in the blind zone can then be identified and bridged the measurement gap between those two traditional models. A calibration rig was used to verify the theoretical analysis and the results indicated that the developed model is capable of providing reliable ultrasonic measurement of lubricant film thicknesses in a wide range.

Variation of reflection coefficient phase with the product of frequency and thickness. The solid line represents the result of complete reflection coefficient phase (Eq. (8)) and the dotted line represents the result of the spring model (Eq. (9)).

Reflection coefficient amplitude and phase spectra of reflected signal from oil films of different thicknesses in the resonant model zone: (a) amplitude spectrum and (b) phase spectrum. The FFT amplitude spectra of reference signal are also shown (dotted line), with arbitrary vertical scale, to demonstrate the bandwidth of the transducer.

Reflection coefficient amplitude and phase spectra of reflected pulse from oil films in blind and spring model zones: (a) amplitude spectrum and (b) phase spectrum. The FFT amplitude spectrum of the reference signal is also shown (dotted line), with arbitrary vertical scale to demonstrate the bandwidth of the transducer.

Comparison of five models of film thickness measurement with the actual film thickness; the minima and zero-crossing methods represent the results from the resonant model (Eq. (3)) by measuring the frequency of minima and zero-crossings, the amplitude |RK| and the phase ΦK method represent the result from spring model (Eqs. (7) and (9)), the phase method Φ represents the result from the complete reflection coefficient phase model (Eq. (8))

The absolute error of actual measured value to predicted one for five experiments by using the reference signal acquired before the experiment. The theoretical reflection coefficient phase spectrum of center frequency is also shown (dotted line), with arbitrary vertical scale.

The absolute error of measured value to actual one for fourth and fifth experiment using the reference signal recorded before and after experiment, respectively. References 1 and 2 represent the reference signal acquired before and after experiment, respectively. The theoretical reflection coefficient phase spectrum of center frequency is also shown (dotted line), with arbitrary vertical scale.

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